Two of the most challenging, yet central, properties are temperature-induced
structural phase transitions in solids and the transport of heat, which in
semiconductors and insulators mainly stems from the lattice vibrations. Both
can be extracted directly from MD simulations [1]}. In the case
of heat transport, this can be obtained from equilibrium MD calculations on
the basis of the Green-Kubo (GK) theory [2]}. This method, based on
the fluctuation-dissipation theorem, is exact at sufficiently high temperatures
where nuclear quantum effects are negligible and is thus superior to lattice
dynamics approaches based on the Boltzmann transport equation (BTE) in crystalline
systems [3]}. AI calculations of thermal transport based on GK
theory, however, have only recently become possible, after a fundamental
issue related to the ill-definition of the microscopic heat flux was
resolved [4]}. Recently, two new theories of thermal transport
have also been developed. These are capable of treating crystalline and
amorphous systems on the same footing and reduce to the BTE in the limit of
periodic solids [5]}, [6]}. Yet, the GK approach carries the
advantage that it accounts exactly for anharmonicity to all orders, while
intrinsically lending itself to a unified description of ordered and disordered
solids, as well as liquids. Nevertheless, the long simulation times and large
supercell sizes required in order to achieve converged results are still
prohibitive for AI calculations. While some approaches have been devised to
overcome this problem [7]}, [8]}, they are not sufficient
to straightforwardly enable calculations of heat transport from first-principles
in any type of solid.
